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The use of short bursts transmissions in modern communication systems is increasing as the use of packet data communication replaces traditional, continuous bit stream data communication. Turbo codes, which revolutionised communication coding, enable the operation of receivers in low signal-to-noise ratio (SNR) conditions, thus increasing the range of operation of the communication system. However, carrier frequency and phase synchronisation, needed for optimal coherent performance of the receiver, still remains an open problem at low SNR conditions for short bursts. A new efficient carrier synchronisation method for turbo coded short packet communication operating at low SNR values is presented. This method is based on maximising a newly invented objective function, the MSSO(Δf, φ) function, which uses the turbo decoder's soft decision outputs to iteratively improve the carrier synchronisation. This method is suitable for non-data-aided acquisition and tracking of the carrier frequency and phase offsets. It is shown, via simulations, that this algorithm achieves the lower bound on bit-error-rate performance of the turbo decoder at very low SNR values.